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A fast and effective breakpoints heuristic algorithm for the quadratic knapsack problem

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2025年第2期323卷 425-440页

作者： Hochbaum, D. S. Baumann, P. Goldschmidt, O. Zhang, Y. Univ Calif Berkeley Ind Engn & Operat Res Dept Berkeley CA 94720 USA Univ Bern Dept Business Adm Engehaldenstr 4 CH-3012 Bern Switzerland Riverside Cty Off Educ Riverside CA 92501 USA

The Quadratic Knapsack Problem (QKP) involves selecting a subset of elements that maximizes the sum of pairwise and singleton utilities without exceeding a given budget. The pairwise utilities are nonnegative, the singleton utilities maybe positive, negative, or zero, and the node costs are nonnegative. We introduce a Breakpoints algorithm for QKP, named QKBP, which is based on a technique proposed in Hochbaum (2009) for efficiently generating the concave envelope of the solutions to the relaxation of the problem for all values of the budget. Our approach utilizes the fact that breakpoints in the concave envelopes are optimal solutions for their respective budgets. For budgets between breakpoints, a fast greedy heuristic derives high-quality solutions from the optimal solutions of adjacent breakpoints. The QKBP algorithm is a heuristic which is highly scalable due to an efficient parametric cut procedure used to generate the concave envelope. This efficiency is further improved by a newly developed compact problem formulation. Our extensive computational study on both existing and new benchmark instances, with up to 10,000 elements, shows that while some leading algorithms perform well on a few instances, QKBP consistently delivers high-quality solutions regardless of instance size, density, or budget. Moreover, QKBP achieves these results insignificantly faster running times than all leading algorithms. The source code of the QKBP algorithm, the benchmark instances, and the detailed results are publicly available on GitHub.

关键词： Combinatorial optimization Quadratic Knapsack problem Breakpoints algorithm Parametric cut greedy algorithm

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Approximation algorithm of maximizing non-submodular functions under non-submodular constraint

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DISCRETE APPLIED MATHEMATICS 2025年 361卷 48-68页

作者： Lai, Xiaoyan Shi, Yishuo Wenzhou Univ Coll Math & Phys Wenzhou 325035 Peoples R China

Nowadays, maximizing the non-negative and non-submodular objective functions under Knapsack constraint or Cardinality constraint is deeply researched. Nevertheless, few studies study the objective functions with non-submodularity under the nonsubmodular constraint. And there are many practical applications of the situations, such as Epidemic transmission, and Sensor Placement and Feature Selection problem. In this paper, we study the maximization of the non-submodular objective functions under the non-submodular constraint. Based on the non-submodular constraint, we discuss the maximization of the objective functions with some specific properties, which includes the property of negative, and then, we obtain the corresponding approximate ratios by the greedy algorithm. What is more, these approximate ratios could be improved when the constraint becomes tight.

关键词： greedy algorithm Non-submodular Non-monotone Non-submodular constraint

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IZ: An improved greedy algorithm for influence maximization under threshold model

IZ: An improved greedy algorithm for influence maximization ...

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Third International Conference on Cyberspace Technology (CCT 2015)

作者： Junrong Wang Yue Hu Xiaozhi Zhang University of Science and Technology Beijing China Institute of Information Engineering Chinese Academy of Sciences Beijing China

Influence maximization is a problem for finding a set of seeds to maximize the spread of information in the network. In this article we bring out a context, which is called influence zone. It's very helpful for us to efficient solve the influence maximization problem. The algorithm which is based on it the original greedy algorithm of efficiency and reduce its running time. We evaluate our algorithms by experiments on serval different synthetic networks. During the experiments we also evaluate the relation of algorithm's efficiency and the influence zone factor.

关键词： greedy algorithms influence zone social networks greedy algorithm Social Networks Social Capital algorithms Runtime threshold models algorithm efficiency

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SEGMENT-WISE ONLINE LEARNING BASED ON greedy algorithm FOR REAL-TIME MULTI-TARGET TRACKING

SEGMENT-WISE ONLINE LEARNING BASED ON GREEDY ALGORITHM FOR R...

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IEEE International Conference on Image Processing

作者： Changhoon Lee Chang D. Yoo Korea Advanced Institute of Science and Technology Department of Electrical Engineering

ISBN: (纸本)9781479983407

This paper proposes a tracklet-based algorithm for online multiple-target tracking. The algorithm performs tracking in three steps: (1) tracklet initialization, (2) tracklet refinement, and (3) tracklet association. Given detection responses, tracklets are initialized by finding a near-optimum path in the min-cost flow network using a greedy-based algorithm. Based on an appearance-based model, the tracklets are refined so that the detection responses within the tracklet become more homogeneous. Finally, the tracklets are linked based on a novel affinity measure, then by optimizing a min-cost flow network with links, the final tracks are generated. For real-time multi-target tracking, every step is processed in a segment-wise manner. On popular public datasets and strictly in an online fashion, the proposed multi-target tracking algorithm performed comparable to that of many state-of-the-art algorithms.

关键词： Multi-target Tracking Online Tracklet greedy algorithm greedy algorithm tracking algorithms

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Joint parameter and time-delay estimation for a class of Wiener models based on a new orthogonal least squares algorithm

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NONLINEAR DYNAMICS 2024年第14期112卷 12159-12170页

作者： Liu, Xinyu Liu, Yanjun Zhu, Quanmin Chen, Jing Jiangnan Univ Sch Internet Things Engn Wuxi 214122 Peoples R China Jiangnan Univ Key Lab Adv Proc Control Light Ind Minist Educ Wuxi 214122 Peoples R China Univ West England Dept Engn Design & Math Bristol BS16 1QY England Jiangnan Univ Sch Sci Wuxi 214122 Peoples R China

This paper focuses on the identification of piecewise-linear Wiener systems alone with multiple inputs, unknown time-delays and system orders in input channels. The parameters and time-delays are jointly estimated by the proposed Householder transformation-based greedy orthogonal least squares (H-GOLS) algorithm. With the help of greedy selection, this algorithm derives the sparse solution. The Householder QR decomposition is employed to reduce the ill-conditioning of the least squares problem, which frequently appears in nonlinear systems. Then we use the Bayesian information criterion to choose the optimal sparsity level for order estimation. Numerical experiments show that the H-GOLS algorithm is more accurate and easier to implement than the LASSO algorithm, which makes it an attractive alternative to identifying sparse Wiener systems within limited data.

关键词： System identification Wiener system Piecewise-linear nonlinearity Time-delay estimation greedy algorithm

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Adaptive Sampling Technique for Free-Form Surface of Aero-Engine Blades Based on Discrete Curvature

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INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING 2025年第2期26卷 325-344页

作者： Huang, Liang Cao, Yan Peng, Runling Li, Hao Wang, Tuo Wei, Guoxin Xian Technol Univ Mechatron Engn Xian 710021 Peoples R China Xian Technol Univ Comp Sci & Engn Xian 710021 Peoples R China Xian KunLun Ind Grp Co LLC Adv Mfg Res Inst Xian 710043 Peoples R China

As the aero-engine blade surface is a typical representative of a free-form surface, its sampling and reconstruction accuracy directly determines the evaluation and correction of subsequent processing technology. In this study, based on a case study of a small engine rotor blade, the blade surface (including concave and convex variations) was divided into thick rectangular meshes based on the idea of mesh subdivision, and the rectangular meshes were refined into primary triangular meshes by Delaunay triangulation. Second, the local Gaussian curvature of the vertices of each primary refined triangle mesh was estimated by combining the Moreton-Sequin method. Then, according to the curvature change in the two connected sampling points on the edge of each primary refined triangle, the adaptive sampling point interpolation along with the curvature change on the boundary of the original triangulation triangle and the densified sampling point distribution, which satisfies the idealized triangulation requirement, were further realized. This approach happens through continuous iteration by introducing a curvature relaxation factor and a greedy algorithm. This method can be used to adaptively adjust the distribution and number of sampling points according to the change in the geometric characteristics of the free-form surface and the curvature distribution of each part. The comparison between this method and the mainstream equidistant sampling method in the blind sampling method and the recent mainstream adaptive sampling method, which uses biquartic B-spline curves, demonstrates that the method proposed in this study can accurately and efficiently represent the complex special-shaped free-form surface in blade free-form surfaces with the fewest sampling points while achieving the highest sampling efficiency and the highest model reconstruction precision.

关键词： Aeroengine blades Free-form surface Adaptive sampling Discrete curvature greedy algorithm

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An Ultra-Wideband Handover System for GPS-Free Bridge Inspection Using Drones

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SENSORS 2025年第6期25卷 1923-1923页

作者： Wang, Ping-Hsiang Wu, Ruey-Beei Natl Taiwan Univ Grad Inst Commun Engn Taipei 106 Taiwan Natl Taiwan Univ Dept Elect Engn Taipei 106 Taiwan

This study proposes an ultra-wideband (UWB) handover system that increases the range of UWB positioning for bridge inspection using an unmanned aerial vehicle (UAV). A bipartite graph and a greedy algorithm are used, and the problem is transformed into vertex coloring to address the challenge of a large number of anchors and insufficient anchor IDs because the area is long and there are numerous beams and columns under the bridge. Simulation and experiment show that the solution reduces the number of anchors that are required from 27 to 14, which significantly saves deployment costs and reduces power consumption.

关键词： ultra-wideband (UWB) handover system UAV bipartite graph greedy algorithm vertex coloring internet of things

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A note on fast deterministic algorithms for non-monotone submodular maximization under a knapsack constraint

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OPERATIONS RESEARCH LETTERS 2025年 61卷

作者： Lu, Cheng Univ Chinese Acad Sci Sch Math Sci Beijing Peoples R China

We present a refined analysis of a variant of the algorithm in the literature for solving the knapsack-constrained submodular maximization problem. By deriving a strong approximation bound for this variant, we reduce the size of the sets requiring enumeration, from two to one, to ensure the final algorithm achieves 1/4-approximation. As a result, we obtain the fastest deterministic algorithm so far which achieves an approximation ratio of 1/4 for the problem.

关键词： Submodular maximization Knapsack constraint greedy algorithm Approximation algorithm

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Seismic resilience evaluation and upgrading framework of UHV converter stations under optimal repair sequence

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EARTHQUAKE SPECTRA 2025年第2期41卷 1801-1821页

作者： Wu, Siyuan Liu, Xiao Xie, Qiang Tongji Univ Coll Civil Engn Shanghai 200092 Peoples R China State Key Lab Disaster Reduct Civil Engn Shanghai Peoples R China

Seismic resilience of ultra-high-voltage converter stations (UHVCSs) has significant implications for reducing post-earthquake damages to power systems. In order to evaluate and improve the seismic resilience of UHVCSs, this article established a seismic resilience assessment framework based on optimal repair sequences. The framework involves a system operation model applicable to the topological characteristics of UHVCSs, and a pathway greedy method to efficiently identify the optimal repair sequence. First, the UHVCS system was partitioned according to the functional coupling relationship of the equipment, and then the system operation model was established based on the enumeration of equipment failure scenarios. Pathways of the system were identified by the connection matrix technique. Then, the optimal repair sequence was found by greedy algorithm at the pathway level. Finally, the statistical characteristics of the seismic resilience of the system were obtained through Monte Carlo sampling. Comparative studies were conducted on the multi-categories and -degrees of strengthening based on the proposed framework, finding upgrading strategies to enhance systems' resilience. This framework avoids the impact of repair sequence uncertainty on resilience-related analysis and has computational feasibility, providing a reference for the formulation of seismic upgrading strategies for UHVCSs.

关键词： UHV converter station seismic resilience assessment operation model repair sequence pathway level greedy algorithm strengthening strategy

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Replicating the performance of a portfolio of stocks using minimum dominating set

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EXPERT SYSTEMS WITH APPLICATIONS 2025年 263卷

作者： Biswas, Subhojit Texas A&M Univ Dept Ind & Syst Engn College Stn TX 77843 USA

Analyzing a portfolio with many assets (stocks) is mathematically challenging. This article considers a large portfolio within a graph theory framework to obtain a tracking portfolio of the actual network. Each asset forms a vertex (node), and the correlation between assets forms the weight of the edges in the graphical network. The large graphical network is efficiently managed using Minimum Dominating Sets (MDS). Finding the MDS of a given portfolio is a well-known NP-hard problem in graph theory. An integer linear programming formulation of MDS is used, and the optimal solution is found using a Gurobi solver. Additionally, greedy and local search algorithms are developed to find the MDS, reducing computation time for extensive portfolios without significantly compromising solution quality. The MDS obtained by the solver and the algorithms are directly compared with an alternative portfolio selection strategy of randomly sub-sampling a certain percentage of the actual portfolio based on size. The expected return of the tracking portfolio is compared to the actual portfolio's expected return graphically, and a statistical significance t-test is performed to confirm the validity of the MDS, . Further, a sensitivity analysis of the expected return of the tracking portfolio obtained from the algorithms is conducted for three different threshold values of the pairwise correlation between assets. Computational results are performed on eight independent instances, with the universe of stocks varying throughout the computation.

关键词： Minimum dominating set Local search algorithm Stock selection greedy algorithm Gurobi solver

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